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IS 14673 (1999) : Liquid flow measurement in open channels
by weirs and flumes - Triangular profile weirs [WRD 1:
Hydrometry]
Jawaharlal Nehru
'Step Out From the Old to the New"
aj^&vi iJii^s:y%K^ isb^^ni^seg
:<>5&i| mT'5K^5?::5:^>^i»l
K^^^iXSVCd^
Satyanarayan Gangaram Pitroda
Invent a New India Using Knowledge
Bhartrhari — Nitisatakam
''Knowledge is such a treasure which cannot be stolen"
^'^^^r
k
BLANK PAGE
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PROTECTED BY COPYRIGHT
IS 14673 : 1999
( Reaffirmed 2004 )
Indian Standard
LIQUID FLOW MEASUREMENT IN OPEN CHANNELS
BY WEIRS AND FLUMES — TRIANGULAR
PROFILE WEIRS
ICS 17.120.0
© BIS 1999
BUREAU OF INDIAN STANDARDS
MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG
NEW DELHIl 10002
May 1999 Price Group 6
Fluid Flow Measurement Sectional Committee, RVD 1
FOREWORD
This Indianiltandard was adopted by the Bureau of Indian Standards, after iSxe draft finalized by the Fluid Flow
Measurem^t Sectional Committee had been approved by the River Valley Division Council
Various methods are adopted for measurement of flow of water in open channels like velocity area method,
slope area method, etc, depending upon the channel, flow conditions, measuring equipment etc* Triangular
profile weirs are used for flow measurement in open channels under steady flow conditions. This Indian Standard
on liquid flow measurement by triangular profile weirs has been prepared based on ISO 4360 : 1984 'Liquid
flow measurement in open channels by weirs and flumes — Triangular profile weirs' and, therefore, is technically
equivalent to the ISO Standard.
For measurem-ent of uncertainties reference shall be m.ade to ISO 5168 : 1978 'Measurem-ent of fluid flow —
Estimation of uncertainty of a flow rate measurement', since corresponding Indian Standard on the subject is
not available as yet.
For the purpose of deciding whether a particular requirement of this standard is complied with, the final value,
observed or calculated, expressing the result of a test or analysis, shall be rounded off in accordance with
IS 2 : 1960 'Rules for rounding off numerical values (revised)\ The number of significant places retained in
the rounded off value should be the same as that of the specifled value in this standard.
IS 14673 : 1999
Indian Standard
LIQUID FLOW MEASUREMENT IN OPEN CHANNELS
BY WEIRS AND FLUMES — TRIANGULAR
nT^/^T7TT "n Tirr7TrkCi
1 SCOPE
This standard specifies methods for the measurement
of the flow of water in open channels under steady
flow conditions using triangular proflle weirs. The
flow conditions considered are steady flows which are
uniquely dependent on the upstreair* head and drowned
flows which depend on downstream as well as
upstream, levels.
2 REFERENCES
The following standards contain provisions which
this standard. At the time of publication the editions
indicated were valid. All standards are subject to
revision, and parties to agreements based on this
standard are encouraged to investigate the possibility
of applying the most recent editions of the standards
indicated below:
IS No. Title
1191 : 1971 Glossary of termiS and symbols used
in connection with the measurement
of liquid flow with a free surface
{first revision)
1 192 : 1981 Velocity area methods for measure-
ment of flow of water in open
channels (first revision)
9116 : 1979 Specification for water stage recorder
(float type)
3 DEFINITIONS AND SYMBOLS
For the purpose of this Indian Standard, the definitions
given in IS 1191 shall apply. The symbols used in this
Indian Standard are given in Annex A.
4 UNiTS OF MEASUREMENT
The units of measurement used by this standard are
seconds and metres.
5 INSTALLATION
Conditions regarding preliminary survey, selection of
site, installation, the approach channel, maintenance,
measurement of head, and stilhng or float wells which
are generally necessary for flow measurement are given
in the following sub-clauses. The particular
requirements for the triangular profiles weirs are given
separately in 8.
5.1 Selection of Site
5.1.1 A preliminary survey shall be made of the
physical and hydraulic features of the proposed site,
to check that it conforms (or may be made to conform)
to the requirements necessary for measurement by a
weir.
5.1.2 Particular attention should be paid to the
following features in selecting the site:
—/
^}
c)
d)
e)
AvailnHilitv rvf nn nHf^niiatp IpnatVi nf ph5ln-
nel of regular cross section;
J- liV VA.i:3VLll^ ......
The avoidance of a steep channel, if possible;
The effects of any increased upstream water
level due to the measuring structure;
Conditions downstream including such in-
fluences as tides, confluences with other
streams, sluice gates, miiidams and other
controlling features which might cause sub-
merged flows;
The impermeability of the ground on which
the structure is to be founded, and the neces-
sity for piling, grouting or other sealing-in
river installations;
The necessity for flood banks to confine the
maximum discharge to the channel;
The stability of the banks and the necessity
for trimming and/or revetment in natural
channels;
The clearance of rocks or boulders from the
bed of the approach channel; and
The effect of wind; wind can have a consid-
erable effect on the flow in a river or over a
weir, especially when these are wide and the
head is small and wheathe prevailing wind
is in a transverse direction.
necessary for satisfactory measurement, the site shall
be rc'ected unless suitable im^rovem.cnts are
practicable,
5.1.4 If an inspection of the stream shows that the
existing velocity distribution is regular, then it may
be assumed that the velocity distribution will remain
satisfactory after the construction of a weir.
g)
h)
J)
k)
IS 14673 : 1999
5.1.5 If the existing velocity distribution is irregular
and no other site for a gauge is feasible, due
consideration shall be given to checking the
distribution after the installation of the weir and to
improving it if necessary.
5J.6 Several methods are available for obtaining a
more precise indication of irregular velocity
distribution: Velocity rods, floats or concentrations of
dye can be used in small channels, the latter being
useful in checking conditions at the bottom of the
channel. A complete and quantitative assessment of
velocity distribution may be made by means of a
current meter. Complete information about the use of
current meters is given in IS 1 192.
5.2 Installation Conditions
5.2.1 General
The complete measuring installation consists of an
approach channel, a measuring structure and a
downstream channel. The conditions of each of these
three components affect the overall accuracy of the
measurements.
Installation requirements include such features as weir
finish, cross-sectional shape of channel, channel
roughness, influence of control device, upstream or
downstream of the gauging structure.
The distribution and direction of velocity, determined
by the features outlined in 5. LI have an important
influence on the performance of the weir.
Once an installation has been constructed, the user
shall prevent any change which could affect the
discharge characteristics.
5.2.2 Approach Channel
On all installations the flow in the approach channel
shall be smooth, free from disturbance and shall have
a velocity distribution as normal as possible over the
cross-sectional area. This can usually be verified by
inspection or measurement. In the case of natural
streams or rivers this can only be attained by having a
long straight approach channel free from projections
either at the side or on the bottom. Unless otherwise
specified in the appropriate clauses, the following
general requirements shall be complied with:
a) The altered flow-conditions due to the con-
struction of the weir might have the effect of
building up shoals of debris upstream of the
structure, which in time might effect the flow
conditions. The likely consequential changes
in the water level shall be taken into account
in the design of gauging stations.
b) In an artificial channel the cross -section shall
be uniform and the channel shall be straight
for a length equal to at least five times its
breadth.
c) In a natural stream or river the cross-section
shall be reasonably uniform and the channel
shall be straight for such a length as to
ensure regular velocity distribution.
d) If the entry of the approach channel is through
a bend or if the flow is discharged into the
channel through a conduit of smaller cross-
section, or at an angle, then a longer length of
straight approach channel may be required to
achieve a regular velocity distribution.
e) There shall be no baffle nearer to the points
of measurement than five times the maximum
head to be measured.
f) Under certain conditions, a standing wave
may occur upstream of the gauging device,
for example, if the approach channel is steep.
Provided this wave is ^t a distance of not less
than 30 times the maximum head upstream,
flow measurement will be feasible, subject to
confirmation that a regular velocity distribu-
tion exists at the gauging station.
5.2.3 Measuring Structure
The structure shall be rigid and watertight and capable
of withstanding flood flow conditions without
distortion and fracture. It shall be at right angles to
the direction of flow and shall conform to the
dimensions given in the relevant clauses.
5.2.4 Downstream of the Structure
The channel downstream of the structure is of no
importance as such if the weir has been so designed
that the flow is modular under all operating conditions.
A downstream gauge shall be provided to measure
tailwater levels to determine when submerged flow
occurs.
In the event of the possibility of scouring downstream
which phenomenon may also lead to the instability of
the structure, particular measure to prevent this
happening may be necessary.
A crest tapping and separate stilling well shall be fitted
if the weir is designed to operate in a drowned
condition or if there is a possibility that the weir may
drown in the future.
The latter circumstances may arise if the altered flow
conditions due to the construction of the weir have
the effect of building up shoals of debris immediately
downstream of the structure or if river works are
carried out downstream at a later date.
6 MAINTENANCE
Maintenance of the measuring structure and the
IS 14673 : 1999
approach channel is important to secure accurate
continuous measurements.
It is essential that the approach channel to weirs should
be kept clean and free from silt and vegetation as far
as practicable for at least the distance specified in 5.2.2.
The float well and the entry from the approach channel
shall also be kept clean and free from deposits.
The weir structure shall be kept clean and free from
clinging debris and care shall be taken in the process
of cleaning to avoid damage to the weir crest.
7 MEASUREMENT OF HEAD
7.1 General
The head upstream of the measuring structure may be
measured by a hook-gauge, point-gauge or staff-gauge
where spot measurements are required, or by a
recording-gauge where a continuous record is required,
and in many cases it is preferable to measure heads in
a separate stilling-well to reduce the effects of water
surface irregularities.
The discharges given by the working equation are
volumetric figures, and the liquid density does not
affect the volumetric discharge for a given head
provided that the operative head is gauged in liquid
of identical density. If the gauging is carried out in a
separate well, a correction for the difference in density
may be necessary if the temperature in the well is
significantly different from that of the flowing liquid.
However, it is assumed herein that the densities are
equal.
7.2 StilHng-Well or Float-Well
Where provided, the stilling-well shall be vertical and
have a free-board of 0.6 over the maximum water level
estimate to be recorded in the well.
It shall be connected to the river by an inlet pipe or
slot, large enough to permit the water in the well to
follow the rise and fall of head without significant
delay.
The connecting pipe or slot shall, however, be as small
as possible, consistent with ease of maintenance, or,
alternatively, shall be fitted with a constriction to damp
out oscillations due to short amplitude waves.
The well and the connecting pipe or slot shall be
watertight where provided for the accommodation of
the float of a level recorder, the well shall be of
adequate diameter and depth to accommodate the float.
The well shall also be deep enough to accommodate
any silt which may enter, without the float grounding.
The float-well arrangement may include an
intermediate chamber between the stilling-well and
the approach channel of similar proportions to the
stilling-well to enable silt and other solids to settle
out. For case of maintenance the pipework may be
valved.
For detailed description of the stilling-well (see
IS 91 16).
7.3 Zero Setting
A means of checking the zero setting of the head-
measuring devices shall be provided, consisting of a
datum related to the level of the weir.
A zero check based on the level of the water when the
flow ceases is liable to serious errors from surface
tension effects and shall not be used.
As the size of the weir and the head on it reduces,
small errors in construction and in the zero setting
and reading of the head-measuring device become of
greater importance.
8 SPECIFICATION FOR THE STANDARD WEIR
8.1 Description
8.1.1 The weir comprises an upstream slope of
1 (vertical) to 2 (horizontal) and a downstream slope
of 1 (vertical) to 5 (horizontal). The intersection of
these two surfaces forms a straight line crest,
horizontal and at right angles to the direction of flow
in the approach channel. Particular attention shall be
given to the crest itself, which shall possess a well-
defined comer of durable construction. The crest may
be made of pre-formed sections, carefully aligned and
jointed, or may have a non-corrodible metal insert, as
an alternative to in-situ construction throughout.
8.1.2 The dimensions of the weir and its abutments
shall conform to the requirements indicated in Fig. 1 .
Weir blocks may be truncated but not so much as to
reduce their dimensions in plan to less than 1 .0 h^^^
for the 1 : 2 slope and 2.0 h^^ for the 1 : 5 slope.
8.2 Location of Head Measurement Section
Piezometers or point-gauge stations for the
measurement of head on the weir shall be located at a
sufficient distance upstream from the weir to avoid
the region of surface drawdown. On the other hand,
they shall be close enough to the weir to ensure that
the energy loss between the section of measurement
and the control section on the weir shall be negligible,
it is recommended that the head-measurement section
shall be located at a distance equal to twice the
maximum head (2 h^^J upsteam of the crest.
8.3 Condition for Modular Flow
8.3.1 Flow is modular when it is independent of
IS 14673 : 1999
UPSTREAM HEAD
STILLING WELLS
CREST TAPPING HEAO
''^^'i:^
'^'^^^^
Fig. 1 Triangular Profile Weir
variations in tailwater level. This requirement is met
when the tailwater total head above crest level is equal
to or less than 75 percent of the upstream total ihead
above crest level.
8.3.2 A significant error in the calculated discharge
will develop if this ratio is exceeded, unless a crest
tapping is provided and two independent head
measurements are made.
8.4 Location of Crest Tapping
8.4.1 The crest tapping shall consist of five to ten
holes of 10 mm diameter drilled in the weir block
with centres 75 mm apart, 20 mm down from the
weir crest on the 1 : 5 slope. Alternatively pipes
may be installed during construction. The edges of
the holes shall not be rounded or burred. The
number of holes shall be sufficient to ensure that
the water level in the stilling-well follows variations
in crest separation pocket pressure without
significant delay.
8.4.2 The optimum position for the crest tapping is at
the centre of the weir crest. The tapping may be off-
centre on weirs wider than 2,0 m provided that the
distance from the centrehne of the crest tapping to
the nearest side wall or pier is greater than 1.0 m.
9 DISCHARGE CHARACTERISTICS
9.1 Equations
9.1.1 The discharge equation for modular flow is:
where
Q - the discharge over the weir, in cubic
metres per second;
C^ = the coefficient of discharge (non-dimen-
sional);
C^ ^ the coefficeint allowing for the effect of
approach velocity
H
3/2
(non-
dimensional);
H = the total head, in metres;
h ^ the breadth of the weir, in metres;
g ~ the acceleration due to gravity, in metres
per second squared; and
h ^ the measured head, in metres.
9.1.2 The discharge equation for drowned flow is;
vV'2
.3/2
where /is the drowned flow reduction factor (non-
dimensional).
9.2 Coefficients
9.2.1 The coefficient C^ for the modular flow equation
is obtained from Fig. 2 where A is the area of the
approach channel.
9.2.2 The combined coefficient C^for the drowned
flow equation is obtained from Fig. 3 where h is the
measured crest tapping head above crest level. Under
modular flow conditions, the value of h Ih is constant
at 0.20 and the value of/is 1.00. Hence, under these
conditions, values of CJ read from Fig. 3 coincide
with values of C^ from Fig. 2.
9.2.3 For water at ordinary temperatures C^ is almost
independent of /i, except at very low heads when fluid
properties influence the coefficient. C^ is given by the
following equation:
Q = 1.163
1-
0.000 3
x3/2
where hh in metres. For practical purposes, C^ can
be set equal to 1.163 for h > 0.1 m,
9.3 Limitations
The following general limitations are recommended:
h > 0,03 m (for a crest section of smooth metal
or equivalent);
h > 0,06 m (for a crest section of fine
IS 14673
1999
P
b
h/p
b/h
>
>
<
>
concrete or
0.06 m;
0.3 m;
3.5; and
2.0.
equivalent);
9.4
Accuracy
9.4.1 The relative accuracy of flow measurements
made with these, weirs depends on the accuracy of the
head measurement, the measurements of dimensions
of the weir and on the accuracy of the coefficients as
they apply to the weir in use.
9.4.2 With reasonable care and skill in the construction
and installation of a triangular profile weir, the
percentage systematic error in the coefficient of
discharge (including C^ and J) may be deduced from
the equation:
X\ = ±
IOC,
/
-9
Numerical values of^'^ are given in Table 1.
The random error depends on the quality of the
research used to determine the coefficient and may be
taken as A^ = ± 0.5 percent in this case.
9,4.3 The method by which the errors in the
coefficients are to be combined with other sources of
errors is given in 10.
.„0-25 0-30 0-35
0.40 045 0&.
V25
T
: I
ji
T
: z
>zo
J
r
: z
. 7
4 JC , f^
\ jL -*
-it
'^A
Tcf^ -
(y^U -
110 V^^
1-10 K^
y
^^
^^
.j.^^
1-05
~ 1 ' .M-i.O'^''.^--'"
7ac,<''''^.rr -
\\%l^^
.— •— — -
"tT^
■tftri — ■.^— a== 1 1 H— I 1 — L
OOO O'OS 0-10 0-1S 0-20
Fk;. 2 CoHFFiciHNT OF Afhroach VnLocn y, C
0^25
■c -c
Fig. 3 Drowned Flow — C /"in Terms of — and — ,/— C —
h 3 V3 " ^
IS 14673 : 1999
IOC,
Table 1 Values of ^\ as a Percentage, in Terms of C^ and/ ^"c = ±1 — r^ - 9
/
(Clause 9.4.2)
n*oi
fAA Af GimKn*Ak*A
Coefncient of Approach Velocity Cy
1.00
1.05
1.10
1.15
1.20
1.25
2/3
>^G
bhxih
/
hA
h^x
0.00
0.24
0.33
0.38
0.42
0.45
1.00
< 0.69
< 0.20
1.00
1.50
2.00
2.50
3.00
3.50
0.95
0,86
0.39
1.53
2.05
2.58
3.11
3.63
4.16
0.90
0.92
0.52
2.11
2.67
3.22
3.78
4,33
4.89
0.85
0.93
0.62
2.76
3.35
3.94
4.53
5.12
5.71
0.80
0.94
0.70
3.50
4.13
4.75
5.38
6.00
6.63
0.75
0.94
0.76
4.33
5.00
5.67
6.33
7.00
7.67
0.70
0.95
0.81
5.29
6.00
6.71
7.43
8.14
8.86
0.65
0.96
0.85
6.38
7.15
7,92
8.69
9.46
10.23
0.60
0.96
0.88
7.67
8.50
9.33
10,17
11.00
11,83
0.55
0.97
0.91
9.18
10.09
11,00
11.91
12.82
13.73
0.50
0.97
0.92
11.00
12,00
13.00
14.00
15.00
16.00
9.4,4 In general, calibration experiments have been
carried otkt on model structures of small dimensions
and when transferred to larger structures there may
be small changes in the discharge coefficients due to
scale effects.
10 UNCERTAINTIES IN FLOW MEASUREMENT
10.1 General
10.1.1 Reference should be made to ISO 5168.
10.1.2 The total uncertainty of any flow measurement
can be estimated if the uncertainties from various
sources are combined. In general, these contributions
to the total uncertainty may be assessed and will
indicate whether the rate of flow can be measured with
sufficient accuracy for the purpose in hand. This clause
is intended to provide sufficient information for the
user of this standard to estimate the uncertainty in a
measurement of discharge.
10.1.3 The eiTor may be defined as the difference
between the true rate of flow and that calculated in
accordance with the equation used for calibrating the
measuring structure, which is assumed to be
constructed and installed in accordance with this
standard. The term ^uncertainty' is used here to denote
the range within which the true value of the measured
flow is expected to lie some ninteen times out of twenty
(95 percent confidence limits).
10.2 Sources of Error
10.2.1 The sources of error in the discharge
measurement may be identified by considering a
generalized form of discharge equation for weirs:
e-(2/3)
^n
Q Csfss
bh
3/2
where
(2/3)^^^ == a numerical constant not subject to
error; and
g == the acceleration due to gravity,
varying from place to place, but the
variation is small enough to be
neglected in flow measurement.
10.2.2 The sources of error which need to be considered
further are:
a) the discharge coefficient Q the velocity of
approach coefficient C^. and the drowned flow
reduction factor/ Numerical estimates and
uncertainties in the combined coefficient
CjCy are given in 9.4;
b) the dimensional measurement of the struc-
tures, for example the breadth of the weir, b\
and
c) The measured head, /i.
10.2.3 The uncertainties in b and h shall be estimated
by the user. The uncertainty in dimensional
measurement will depend upon the accuracy to which
the device as constructed can be measured: in practice,
this error may prove to be insignificant in comparison
with other errors. The uncertainty in the head will
depend upon the accuracy of the head-measuring
device, the determination of the gauge zero and upon
the technique used. The error may be small if a vernier
or micrometer instrument is used, with a zero
determination of comparable precision.
10,3 Kinds of Error
10.3.1 Errors may be classified as random or
systematic, the former affecting the reproducibility
(precision) of measurement and the latter affecting its
true accuracy.
IS 14673 : 1999
10.3.2 The standard deviation of a set of n
measurements of a quantity Kunder steady conditions
may be estimated from the equation:
sr =
^1/2
where Y is the arithmetic mean ofthe/i measurements.
Tne standard deviation of the mean is then given by:
Sy
and the uncertainty of the mean is twice s^ (to 95
percent confidence level)**. This uncertainty is the
contribution of the observations of Y to the total
uncertainty.
10,3.3 A measurement may also be subject to
systematic error; the mean of very many measured
values would thus still differ from the true value of
the quantity being measured. An error in setting the
zero of a water level gauge to invert level, for
example, produces a systematic difference between
the true mean measured head and the actual value.
As repetition of the measurement does not eliminate
systematic errors, the actual value could only be
determined by an independent measurement known
to be more accurate.
10.4 Errors in Coefficient Value
10.4.1 The values of the discharge coefficients C^
and C^ quoted in this standard are based on an
appraisal of experim.ents, which may be presumed
to have been carefully carried out, with sufficient
repetition of the readings to ensure adequate
precision. Random and systematic errors from this
source are small, However, when measurements are
made on other similar installations, systematic
discrepancies between coefficients of discharge may
well occur, which may be attributed to variations in
the surface finish of the device, its installation, the
approach conditions, the scale effect between model
and site structure, etc.
10.4.2 The uncertainty in the coefficients quoted
in the preceding clauses of this standard are based
on a consideration of the deviation of experimental
data from various sources from the equations
given. The suggested uncertainties thus represent
the accumulation of evidence and experience
available.
'* This factor of two assumes that n is large, for « = 6, the factor should
be 2.6; /I -8 requires 2,4; n = 10 requires 2.3; « = 15 requires 2.1,
10.5 Uncertainties in Measurements Made by the User
10.5.1 Beth random and systematic errors will occur
in measurements made by the user.
10.5.2 Since neither the method of measurement nor
the way in which they are to be made are specified, no
numerical values can be suggested for uncertainties
in this category; they shall be estimated by the user.
For example, consideration of the method of measuring
the weir width should permit the user to estimate the
uncertainty in this quantity.
10.5.3 The uncertainty in the gauged head shall be
determined fi^om an assessment of the separate sources
of uncertainty, for example, the uncertainty of the zero
setting, wind set-up, the gauge sensitivity, backlash
in the indicating equipment (where appropriate), the
residual uncertainty in the mean of a series of
measurements (where appropriate).
10.6 Combination of Uncertainties
10.6.1 The total systematic or random uncertainty is
the resultant of several contributory uncertainties, which
may themselves be composite uncertainties. Provided
the contributing uncertainties are independent, small
and numerous, they may be combined together to give
overall a random (or systematic) uncertainty at the 95
percent confidence level.
10.6.2 All sources contributing imcertainties will have
both random, and system.atic com^ponents. However,
in some cases either the random or the systematic
component may be predominant and the other
component can be neglected by comparison.
10.6.3 Because of the different na^are of random and
systematic uncertainties, they should not normally be
combined with each other. However, with the
provisions of 10.6.1 random uncertainties from
different sources may be combined together by the root-
sum of squares rule; systematic uncertainties from
different sources may be similarly combined.
10.6.4 The percentage random uncertainty A* in the rate
of flow m.ay be calculated from, the following equation:
Xij=±4xfir^^+^^^
where
X' ^ the percentage random uncertainty in
X'^ ^ the percentage random uncertainty in 6;
X'^^ = the percentage random uncertainty in h.
In the above, A^^ == lOOx^
b
and X{,^(,Xl,' + ,Xi,'+ + X-^f
IS 14673 : 1999
where
1 ^h' » 2^h'
x^
the random uncertainty in breadth
measurement;
etc, are percentage random
uncertainties in head measurement
{see 10.5.3); and
the percentage random uncertainty of
the mean if a series of readings of
head measurement are taken at
constant water level.
The term^^ is easily estimated if, for example, a point
gauge is used for water level measurement. For
continuous or digital recording equipment, the random
uncertainty in reading a given water level can be
assessed by laboratory tests on the equipment.
10.6.5 The percentage systematic uncertainty X"' in
the rate of flow may be calculated from the foUowmg
equatidh:
X\ - ±V^"^^X"g + 1.5^X'
where
X" = the percentage systematic uncertainty in
X*'^ == the percentage systematic uncertainty in b\
X'\ = the percentage systematic uncertainty in h;
In the above X\ = (,X"^ + 2^i + f^
where ivt'*h>2^*h ^^^' ^^^ percentage systematic
uncertainties in head measurement {see 10.5.3).
10.7 Presentation of Results
10.7.1 Although it is desirable, and frequently
necessary, to list total random and total systematic
uncertainties separately, it is appreciated that simpler
presentation of results may be required.
For the purpose, random and systematic uncertainties
may be combined as shown in ISO 5168
Xg^±p(^^HX^'
11 EXAMPLES
1 LI Example 1
The following is an example of the computation of
the flow rate and associated uncertainty in a single
measurement of flow using a triangular profile weir,
for modular flow conditions. The crest height;? above
the bed of the approach channel is 1 m and the gauged
head h is 0.67 m. The breadth of the weir crest b and
the breadth of the approach channel B are both equal
to 10 m.
11.1.1 For calculation of the discharge, the equation
in 9.1.2 is used. Since the guaged head h is greater
than 0. 1 m, C^ = 1 . 1 63 . For modular flow the drowned
flow reduction factor equals 1.
1L1*2 In order to read C^ from Fig. 2, it is necessary
to evaluate 2/3 ^JlThC^bhf A where A is the cross-
sectional area of flow in the approach channel, in this
case equal to B {h-^p) or 10 (0.67 + 1) = 16.7 m^
Then
2/3 V273Q6/i/ ^ = 2/37273x1.163x10x0.67/ 16.7
= 0.254
With this value, from Fig. 2, C - 1,054.
11.1.3 Using the equation in 9.1.2:
Q={2/3f^C,C,f^bh
3/2
x3/2
3/2
=(2/3)'''^xl.l63xL054xlxV9.81xl0x(0.67)
= 11.46m^/s.
1LL4 To calculate the uncertainty in this value of ^,
the uncertainties in the coefficient values are first
determined:
(from 9.4)
(from 9.4)
X'^ =±0.5 percent
^ pO..I.054 ^
- ±1.54 percent
11.1.5 Assuming that several measurements of breadth
are taken, the random component of uncertainty in
width measurement is likely to be negligible. The
systematic uncertainty in length measurement is
assumed in this case to be O.O-l m. Accordingly,
X^^O
Xi;^ — x 100= ±0.1 percent
11.1.6 With the equipment used it had been
demonstrated that the gauge zero could be set to within
±3 mm. This is a systematic uncertainty; however the
magnitude of the uncertainty shall be related to the
IS 14673 : 1999
equipment used. There is no random uncertainty
associated with the zero setting error, because, until
the zero is reset the true zero will have the same
magnitude and sign. Therefore,
l^H=0
xi; =
\^h
0.003
0.67
X 100^ 0.45 percent
11.L7 Uncertainties associated with different types of
water level observations equipment can be determined
by careful tests under controlled conditions. The random
component of uncertainty can be determined by carrying
out a series of readings at a given water level; however,
in order to distinguish the random uncertainty from
other sources of uncertainty it is necessary that these
tests should be carried out with the water level always
rising (or falling). For the equipment used the random
component of uncertainty in water level measurement
was approximately ±1 mm. Systematic uncertainties in
water level measurement occur due to backlash, tape
stretching, etc. Where possible, corrections should be
applied, but controlled tests for given types of equipment
will indicate the magnitude of the residual systematic
uncertainty. In the present case this was approximately
±2.5 mm. Accordingly
X'^ = ^^^x 100 = O.lSpercent
2^ h
X'l^±
0.67
0.0025
2-^ h
0.67
xlOO = 0.37 percent
11. L8 The combination of individual uncertainties to
obtain the overall uncertainty in discharge may be
carried out as follows:
The uncertainties in water level measurement are
assuming X'^ is negligible:
Xh-^S \Xh + 2^h
= ± ^/o + ol? = ± O.l 5 percent
x;; = ±yl,x'f;'^2^f
= ±^0.45^ +0.37^ =±0.58 percent
Total random uncertainty in discharge measurement:
xl/2
X^=±{x^'+Xi'^l5'X{,')
-±(0.5^+0 + 2.25x0.15^)
= ±0,55 percent.
1/2
Total systematic uncertainty in discharge
measurement:
X'q =±{X'l +^'^ + 1.5^ X{:^f^
= ±(1.54^+0.1^+2.25x0.58^)*^^
= ±1.77 percent.
In order to facilitate a simple presentation, the random
and systematic uncertainties may be combined by the
root-sum of squares rule
Xq = ±7oi?+l77^ = ±1.85 percent
The flow rate Q may be reported as
1 1 .46 mVs ± 1 .85 percent; Random uncertainty = ±0.55
percent.
11.2 Example 2
The following is an example of the computation of
the flow rate and associated uncertainty in a single
measurement of flow using a triangular profile weir,
for drowned flow conditions. The crest height p is
1 m, and the gauged height h is 2.2 m. The crest
tapping head h is 1 .7 m. The breadth of weir crest b
and the breadth of the approach channel B are both
equal to 10 m. The same digital punched type recorder
is assumed as in the previous example.
1 1.2.1 Since the gauged head h is greater than 0. 1 m,
C - 1.163.
d
11.2.2 In order to read C^from Fig. 3, it is necessary
to evaluate llZ^inC^bhl A and h Ik
A - 10(2.2+ l)-32m^
Then
2/3 V273Q^/(/ ^ = 2/ 3V27Ix 1.163x10x2.2/32
= 0.436
Also, /iZ/i - 1.7/2.2 = 0.773
Then, from Fig. 3, C/- 0.88.
11.2.3 Using the equation in 9.1.2
Q--{2/3f^C,^Cj4ghh
3/2
.3/2
e = (2/3)'^" xl.l63x0.88V9.81x 10x2.2
= 56.94 m^/s
3/2
10
IS 14673 : 1999
11.2.4 The uncertainities in the coefficient values are
calculated as follows:
X^ =^± 0.5 percent (from 9.4)
Referring to Table i, with h Ih ^ 0.113 and
in^imc^hhl A = 0.436, by interpolation
xl = ±7.6 percent approximately.
11.2.5 As in the previous example,
4-0
X^= ±0.1 percent.
11.2.6 Assuming that the gauge zero could be set to
within ± 3 mm:
J X'^ = +£:5^ x\m^ ± 0.14 percent
11.2.7 Using the same uncertainties associated
with the water level equipment as in the pcvious
example.
2^h
-> xi:
0.001
2.2
0-002 5
xlOO - ±0.045 percent
xlOO^ ±0.1 I percent
11.2.8 The resulting uncerTainties it' '.vatcr level
measurement arc, assuming A",^, is negligible.
X{^^±^^Xl^+ 2^A^ - ±^0 + 0.045^
= ±0.05 percent
X^^±^^Xf^ 2^A^ = ±^0.14^0.11^
= ±0.1 8 percent
Total random uncertainty in discharge measurement
-±(0.5^+0 + 2.25x0.05^)
= ±0.51 percent
Total systematic uncertainty in discharge measurement
1'2
1/2
X'^^±(xf^x;^'^Wxf]
= ±(7.6^+0.1^+2:25x0.18^)
= ±7.61 percent
For simplicity of presentation, the random and
systematic components of uncertainty may be combmed:
Xq =±^0.51- +7.61- = ±7.63 percent
The flow rate may be reported as:
56.94mVs±7 63 percent;
Random uncertainty = ± 0.51 percent,
II
IS 14673 : 1999
ANNEX A
{Clause 3)
SYMBOLS
Symbol
Designation
Units of
Measurement
A
area of approach channel
m^
B
breadth of approach channel
m
b
breadth of weir crest
m
Ci
coefficient of discharge
non-dimensional
Cv
coefficient of approach velocity
non-dimensional
/
drowned flow reduction factor
non-dimensional
g
acceleration due to gravity
m/s^
H
total (energy) head above crest level
m
h,hi
upstream gauged head above crest level
m
h2
downstream gauged head above crest level
m
K
measured crest tapping head above crest level
m
n
number of measurement in a set
—
P
height of weir (difference between mean bed level and crest level)
m
Q
total discharge
mVs
■sy
standard deviaton of a quantity Y
~
'y
standard deviaton of the mean
—
X
over percentage uncertainty
%
^b
percentage uncertainty in h
%
Xc
percentage uncertainty in Cd C^f
%
x^
percentage uncertainty in h
%
■^m
percentage uncertainty in the mean of a set of head measurement readings
%
^0
percentage uncertainty in Q
%
b
random uncertainty in breadth measurement
m
Superscrif
>ts to X : ' denotes random components of uncertainty
" denotes systematic components of uncertainty
12
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